On the rigidity of back-to-back top quark pairs in e+e− annihilation Original Research Article

We consider the effect of gluon radiation on the energy of top/antitop quarks and on the anticollinearity of top-antitop quark pairs produced in e+e− annihilation. Our results are presented in terms of the Eq-dependence of the ttg cross section and the dependence on the cosine of the the opening angle θ12 between top and antitop for a center of mass energy of √q2 = 500 GeV. We then go on to determine mean values for the top quarkʹs energy as well as its longitudinal and transverse projections, and for the deviation of sin θ12 and cos θ12 from the anticollinearity limits sin θ12 = 0 and cos θ12 = −1. For a center of mass energy of 500 GeV we obtain 〈Eq〉 = 248.22 GeV, 〈EL〉 = 247.24 GeV and 〈ET〉 = 4.70 GeV. Thus, at this energy gluon radiation causes a total average energy loss of 0.71% of the top quarkʹs energy. The average energy loss in the longitudinal direction is 1.06% and the average energy gain in the transverse direction is 1.88%. These percentage figures go up to 3.77%, 5.19% and 6.06%, respectively, at 1000 GeV. For the mean of the acollinearity angle θ12 = 1800 − θ12 we obtain 〈θ12〉 = 1.25° at 500 GeV, the value of which goes up to 4.620 at 1000 GeV. From an analysis of the transverse momentum of the top we find that the mean transverse momentum of the top stays close to the mean total momentum of the gluon in the energy range from threshold to 1000 GeV showing that the gluon momentum has a large mean transverse component in this energy range.